Assessment and Optimization of the Gamma-Weighted Two-Stream Approximation

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Abstract
The two primary foci of this note are to assess the ability of the multilayer gamma-weighted two-stream approximation (GWTSA) to compute domain-averaged solar radiative fluxes and to demonstrate how its execution time can be reduced with negligible impact on performance. In addition to the usual parameters needed by a 1D solar code, the GWTSA requires ν ∈ R+, which depends on both the horizontal mean and mean logarithm of cloud water content. Reduced central processing unit (CPU) time is realized by simply rounding ν to the nearest whole number, denoted as [ν]. The experiment reported on here uses 120 fields generated by a 2D cloud-resolving model simulation of an evolving tropical mesoscale convective cloud system. Benchmark calculations are provided by the independent column approximation (ICA), and results are also shown for the conventional two-stream model. The full GWTSA yields time- and domain-averaged broadband top-of-atmosphere albedo and surface absorptance values of 0.32 and 0.49, which are very close to the ICA values of 0.32 and 0.47. Correspondingly, the GWTSA using [ν] produces 0.34 and 0.46. In contrast, the conventional two-stream’s estimates are 0.56 and 0.20. While mean heating rate errors for the conventional two-stream average about −0.5 K day−1 near the surface and almost +2 K day−1 at 10 km, they are diminished at both altitudes to ∼0.25 K day−1 for the GWTSA regardless of whether ν or [ν] is used. For this simulation, the GWTSA using [ν] requires just ∼25% more CPU time than the conventional two-stream approximation.

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